Distributed Shape Formation of Multirobot Systems via Dynamic Assignment

In this article, we propose a fully distributed algorithm that leverages the concept of exploration behavior to achieve the shape formation control of multirobot systems. Here, the exploration behavior means that each robot can actively explore the unoccupied goal locations in the shape, thus removing the prior goal assignment for each robot and increasing the system's flexibility. This exploration behavior can be realized by mimicking the negative phototaxis observed in nature. To be specific, each robot can dynamically choose multiple goal locations with the light intensity less than a given value in its sensing range, which can be computed by local information. Furthermore, we employ local peer-to-peer communications to propagate the unoccupied goal, and then the trapped robots will move toward the remote unoccupied goal, thus ensuring and speeding up the convergence. In the meantime, the control command can be obtained by solving a constrained optimization function. Moreover, the theoretical analysis reveals that our algorithm can drive robots to achieve the desired shape if the initial distance between robots' positions and goal locations satisfies the distance condition. Finally, simulation and physical experiment results demonstrate adaptability to complex shapes and swarm sizes and high efficiency of our algorithm.